Question

Tan22.5°with explanation

Answer 1

we know that [ ( 1- cos 2x ) / ( 1+ cos 2x) ] = tan2x therefore => tan 22.5 = square root ( tan2 22.5) => square root [ (1 - cos 45 ) / (1+ cos 45) ] => square root [ ( 1- (1/ square root 2) ) / ( 1 + (1/ square root 2) ) ] => squareroot [ ( ( squareroot 2) - 1 ) / ( (squareroot 2) + 1 ) ] Now rationalising by ((squareroot 2) - 1 ) , we get => ( ( sqaure root 2 ) - 1) 2 / ( ( sqaureroot 2 )2 - 12 ) { using (a+b)(a-b) = a2 - b2 } => ( ( sqaure root 2 ) - 1 ) / (2-1) => ( sqaure root 2 ) - 1 Answer